(5/3x)-2=x+6

Solution for (5/3x)-2=x+6 equation:

(5/3x)-2=x+6

We move all terms to the left:

(5/3x)-2-(x+6)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/3x)-(x+6)-2=0

We get rid of parentheses

5/3x-x-6-2=0

We multiply all the terms by the denominator


-x*3x-6*3x-2*3x+5=0

Wy multiply elements

-3x^2-18x-6x+5=0

We add all the numbers together, and all the variables

-3x^2-24x+5=0

a = -3; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·(-3)·5
Δ = 636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{159}}{2*-3}=\frac{24-2\sqrt{159}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{159}}{2*-3}=\frac{24+2\sqrt{159}}{-6}
$